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Abstract:

A passive structural system includes a structural element which may be
subjected to energy which gives rise to vibration in the element. At
least one bi-stable sub-structure is coupled to the element. Each
bi-stable sub-structure has two stable equilibrium states between which
the sub-structure can physically transition when subjected to a
sufficient amount of energy which gives rise to vibration in the element,
with each bi-stable sub-structure arranged to dissipate at least a
portion of the energy and thereby damp the vibration in the structural
element when it transitions from one equilibrium state to the other. The
passive structural system may also be intentionally mistuned such that
when subjected to energy which gives rise to vibration, the vibration
energy is substantially confined to localized regions within the system.
The bi-stable structures are then located in the localized regions and
arranged to dissipate the localized vibration energy.

Claims:

1. A passive structural system, comprising: a structural element which
may be subjected to energy which gives rise to vibration in said
structural element; at least one bi-stable sub-structure coupled to said
structural element, each of said bi-stable sub-structures having two
stable equilibrium states between which said sub-structure can physically
transition when subjected to a sufficient amount of said energy which
gives rise to vibration in said structural element, each of said
bi-stable sub-structures arranged to dissipate at least a portion of said
energy and thereby damp the vibration in said structural element when it
physically transitions from one of said equilibrium states to the other.

2. The system of claim 1, wherein each of said bi-stable sub-structures
comprises a movable element which has an associated mass and may be in
either of said two stable equilibrium states or transitioning between
said states, the inertia of said mass when subjected to said energy which
gives rise to vibration in said structural element causing said bi-stable
sub-structure to transition from one of said stable equilibrium states to
the other.

3. The system of claim 2, said bi-stable sub-structure arranged such that
said associated mass consists solely of the inherent mass of said movable
element.

4. The system of claim 2, further comprising one or more additional
masses coupled to said movable element, said bi-stable sub-structure
arranged such that said associated mass consists of the inherent mass of
said movable element plus the one or more additional masses coupled to
said movable element.

5. The system of claim 4, wherein one of said additional masses is
coupled to the point of said movable element which exhibits the greatest
amount of displacement when said bi-stable sub-structure transitions from
one of said equilibrium states to the other.

6. The system of claim 2, wherein each of said movable elements is
dome-shaped or arch-shaped.

7. The system of claim 1, wherein each of said bi-stable sub-structures
comprises a movable element comprising silicone rubber, composite
laminates, or flexible metal.

8. The system of claim 1, wherein each of said stable equilibrium states
has an associated equilibrium position relative to a nominal center
position between said equilibrium positions, each of said bi-stable
sub-structures having an associated relationship between reaction force
and the displacement between said bi-stable sub-structure and said
nominal center position and arranged such that when said bi-stable
sub-structure is acted upon by a force, said reaction force is in the
same direction as the action force and the sub-structure enters a
negative stiffness region where the slope of the reaction force over
displacement is negative.

9. The system of claim 1, wherein said structural element is a hollow
structure having an associated longitudinal axis, each of said bi-stable
sub-structures comprising an buckled column which spans the hollow
interior of said structural element and is oriented perpendicular to said
tube's longitudinal axis.

10. The system of claim 9, wherein each of said buckled columns is a
constrained, buckled column.

11. The system of claim 1, wherein each of said bi-stable sub-structures
comprises a movable element comprising a bi-stable composite laminate
plate.

12. The system of claim 1, wherein a plurality of said bi-stable
sub-structures are coupled to said structural element periodically.

13. The system of claim 1, wherein each of said bi-stable sub-structures
has associated characteristics which govern the conditions under which
said bi-stable sub-structure transitions from one of said equilibrium
states to the other, said characteristics tailored to provide a desired
amount of damping for said structural element.

14. The system of claim 1, wherein said passive structural system is
intentionally mistuned such that when said passive structural system is
subjected to energy that gives rise to vibration in said structural
system, said vibration energy is substantially confined to localized
regions within said structural system, said bi-stable structures located
in said localized regions and arranged to dissipate said localized
vibration energy.

15. A passive structural system, comprising: a structural element;
periodic appendage sub-structures attached to said structural element and
mistuned such that when said structural system is subjected to energy
that gives rise to vibration in said structural system, said vibration
energy is substantially confined to localized regions within said
structural system; and damping elements in said localized regions
arranged to dissipate said localized vibration energy.

16. The system of claim 15, wherein said periodic appendage
sub-structures are rings that are coupled to and encircle said structural
element.

17. The system of claim 16, wherein said structural element is
tube-shaped and said encircling rings are distributed at equal intervals
along the axial length of said tube.

18. The system of claim 16, wherein one of said damping elements
comprises a layer between each of said encircling rings and said
structural element, each of said layers comprising a coupling elastic and
damping material and arranged to couple a respective encircling ring to
said structural element.

19. The system of claim 18 wherein said layers have respective material
properties, at least one of which varies from layer to layer, said
variance resulting in at least a portion of said mistuning.

20. The system of claim 19, wherein said material property which varies
from layer to layer comprises stiffness and/or damping coefficient.

21. The system of claim 18, wherein said structural element is
tube-shaped and said encircling rings are distributed along the axial
length of said tube, said encircling rings arranged to move along said
tube's longitudinal axis when subjected to vibration and thereby
dissipate at least a portion of said vibration energy.

22. The system of claim 16, wherein said encircling rings have respective
parameters, at least one of which varies from ring to ring, said variance
resulting in at least a portion of said mistuning.

24. The system of claim 16, wherein said structural element is
tube-shaped and said encircling rings are distributed at unequal
intervals along the axial length of said tube, said unequal intervals
resulting in at least a portion of said mistuning.

25. The system of claim 15, wherein said structural element is a hollow
tube-shaped structure, at least one of said damping elements comprising
bi-stable sub-structures located within and along the axial length of
said tube at respective ones of said localized regions, said bi-stable
sub-structures having two equilibrium states and arranged to transition
from one equilibrium state to the other when subjected to said vibration
energy and thereby dissipate at least a portion of said vibration energy.

26. The system of claim 25, wherein each of said bi-stable sub-structures
comprises an buckled column which spans the hollow interior of said tube
and is oriented perpendicular to said tube's longitudinal axis.

27. The system of claim 26, wherein each of said buckled columns is a
constrained, buckled column.

28. The system of claim 25, wherein each of said bi-stable sub-structures
comprises a pair of buckled columns which intersect to form an X-shaped
pattern, each of said buckled columns arranged to span the hollow
interior of said tube and oriented perpendicular to said tube's
longitudinal axis.

29. The system of claim 28, wherein each of said bi-stable sub-structures
further comprises a concentrated mass at the intersection of said buckled
columns, the motion of said buckled columns and said concentrated masses
during said transitions between said equilibrium states dissipating at
least a portion of said vibration energy.

30. The system of claim 15, further comprising a structural link which
couples said periodic appendage sub-structures together.

31. The system of claim 30, wherein said periodic appendage
sub-structures are rings that are coupled to and encircle said structural
element, said structural link coupling said encircling rings together.

32. The system of claim 30, wherein said structural element is a hollow
tube-shaped structure, said at least one of said damping elements
comprising bi-stable sub-structures located along the axial length of
said tube at respective localized regions within said tube, said
structural link coupling said encircling bi-stable sub-structures
together.

[0003] This invention relates to high stiffness passive structures, and
particularly to damping techniques suitable for use with such structures.

[0004] 2. Description of the Related Art

[0005] Structural elements are used for a myriad of purposes. Such
elements often need to provide high stiffness; one class of structure
system which exhibits extreme stiffness is made from metals such as
aluminum or steel. Such structures are often subjected to vibration and
shock. However, due to the structure's characteristic stiffness, it may
lack sufficient damping capability to mitigate the vibration, which may
result in the failure of the structure or any attached equipment.

[0006] Another class of structure system employs conventional
visco-elastic (damping) materials to mitigate shock and vibration, but
this can result in the structure having a stiffness which is inadequate
to the needs of a major structural element.

[0007] Vibration suppression in many engineering systems is achieved via
active control. Common active vibration control methods require the use
of sensors and actuators (such as piezoceramic patches) in the system,
and need additional input power to operate. However, most active
vibration systems have high costs and are technologically complex, and
may be impractical for use in difficult environments such as the open
ocean.

SUMMARY OF THE INVENTION

[0008] A structural system is presented which overcomes the problems noted
above, providing high stiffness and high damping with a passive system.

[0009] The present system includes a structural element which may be
subjected to energy which gives rise to vibration in the element. At
least one bi-stable sub-structure is coupled to the element. Each
bi-stable sub-structure has two stable equilibrium states between which
the sub-structure can physically transition when subjected to a
sufficient amount of energy which gives rise to vibration in the element,
with each bi-stable sub-structure arranged to dissipate at least a
portion of the energy and thereby damp the vibration in the structural
element when it transitions from one equilibrium state to the other.

[0010] The passive structural system may also be intentionally mistuned
such that when subjected to energy which gives rise to vibration, the
vibration energy is substantially confined to localized regions within
the system. The bi-stable structures are then located in the localized
regions and arranged to dissipate the localized vibration energy.

[0011] Further features and advantages of the invention will be apparent
to those skilled in the art from the following detailed description,
taken together with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

[0012] FIG. 1 is a diagram illustrating the principles of a passive
structural system per the present invention.

[0013] FIG. 2 is a graph depicting a negative stiffness region for a
passive structural system per the present invention.

[0014] FIGS. 3a and 3b are sectional and perspective views, respectively,
of one possible embodiment of a bi-stable sub-structure per the present
invention.

[0015] FIGS. 4a and 4b are sectional and perspective views, respectively,
of another possible embodiment of a bi-stable sub-structure per the
present invention.

[0016] FIGS. 5a and 5b are views of another possible embodiment of a
bi-stable sub-structure per the present invention, in each of its stable
equilibrium states.

[0017] FIG. 6 provides several views of one possible embodiment of a
passive structural system per the present invention.

DETAILED DESCRIPTION OF THE INVENTION

[0018] The present passive structural system is capable of attaining high
stiffness and high damping simultaneously, by employing bi-stable
sub-structures which serve to damp vibration in the system. A diagram
illustrating the principles of a passive structural system per the
present invention is shown in FIG. 1.

[0019] The present passive structural system comprises a structural
element 10 which may be subjected to energy 12 ("external excitation")
which gives rise to vibration in the structural element. At least one
bi-stable sub-structure 14 is coupled to the structural element. Each
bi-stable sub-structure has two stable equilibrium states 16, 18 between
which the sub-structure can physically transition when subjected to a
sufficient amount of energy 12, such that the sub-structure dissipates at
least a portion of energy 12 and thereby damps the vibration in
structural element 10 when it physically transitions from one equilibrium
state to the other.

[0020] Each of the stable equilibrium states has an associated equilibrium
position (16, 18) relative to a nominal center position 20 between the
stable equilibrium states. Each bi-stable sub-structure has an associated
relationship between reaction force and the displacement between the
sub-structure and nominal center position 20, and is arranged such that
when the bi-stable sub-structure is acted upon by a force, the reaction
force is in the same direction as the action force and the sub-structure
enters a negative stiffness region where the slope of the reaction force
over displacement is negative. This is illustrated in the graph shown in
FIG. 2, which plots reaction force, displacement, and potential energy.
As external excitation causes the sub-structure 14 to move from one of
its equilibrium positions (e.g., position 16) towards its nominal center
position, it enters a `negative stiffness region` 22 and `snaps-through`
to its other equilibrium position (e.g., position 18). The transient,
unstable negative stiffness condition can produce a large loss factor,
especially if the mass of the transitioning sub-structure is also large.

[0021] Each of the bi-stable sub-structures includes a movable element
which may be in either of the two stable equilibrium states or
transitioning between the states, and which has an associated mass. The
inertia of the mass when subjected to energy which gives rise to
vibration in the structural element causes the sub-structure to
transition from one of the stable equilibrium states to the other. The
bi-stable sub-structures can be arranged such that the associated mass
consists solely of the inherent mass of the movable element.
Alternatively, one or more additional masses can be coupled to the
movable element, such that the bi-stable sub-structure's associated mass
consists of the inherent mass of the movable element plus the mass of the
additional masses. At least one of the additional masses is preferably
coupled to the point of the movable element which exhibits the greatest
amount of displacement when the bi-stable sub-structure transitions from
one of its equilibrium states to the other, as this provides the greatest
amount of damping.

[0022] The bi-stable sub-structures can take any of a number of forms. One
possible embodiment is depicted in the sectional and perspective views
shown in FIGS. 3a and 3b, respectively. Here, the bi-stable sub-structure
30 consists of a moveable element 32 which is dome-shaped. The first of
the sub-structure's two equilibrium states is as shown in FIG. 3a, with
the peak of the dome facing downward; the second equilibrium state would
be the mirror image of FIG. 3a, with the peak of the dome facing upward.
An additional mass 34 is preferably coupled to the peak of the dome,
which is the point of greatest displacement when movable element 32
transitions between equilibrium states. One or more of bi-stable
sub-structures 30 are coupled to a structural element 36 and serve to
dampen the vibration that arises in element 36 due to external excitation
energy.

[0023] Another possible embodiment is depicted in the sectional and
perspective views shown in FIGS. 4a and 4b, respectively. Here, the
bi-stable sub-structure 40 consists of a moveable element 42 which is
arch-shaped. The first of the sub-structure's two equilibrium states is
as shown in FIG. 4a, with the peak of the arch facing downward; the
second equilibrium state would be the minor image of FIG. 4a, with the
peak of the arch facing upward. An additional mass 44 is preferably
coupled to the peak of the arch, which is the point of greatest
displacement when movable element 42 transitions between equilibrium
states. One or more of bi-stable sub-structures 40 are coupled to a
structural element 46 and serve to dampen the vibration that arises in
element 46 due to external excitation energy.

[0024] Another possible embodiment is shown in FIGS. 5a and 5b, which show
the bi-stable sub-structure 50 in each of its two equilibrium states.
Here, the moveable element comprises a bi-stable composite laminate
plate. When the plate `snaps-through` as it transitions from one
equilibrium state to the other in response to vibration energy, a
substantial damping force is realized.

[0025] The moveable element needs to be made from a material which is
stiff enough so that some force is required to make it transition between
equilibrium states, yet flexible enough to allow the transition. Suitable
materials include silicone rubber, composite laminates, and flexible
metal.

[0026] Each bi-stable sub-structure has associated characteristics which
govern the conditions under which it transitions from one of its
equilibrium states to the other. These characteristics may be tailored to
provide a desired amount of damping for a given structural element.

[0027] The bi-stable sub-structures may be coupled to any portion of the
structural element to provide damping. For example, as shown in FIGS. 2a,
2b, 3a and 3b, the sub-structures can be located at one end of the
structural element. Another possibility is to couple the bi-stable
sub-structures to the structural element periodically (as shown in FIG.
6, discussed below).

[0028] A typical application for a passive structural system as described
herein is shown in FIG. 6, in which three structural elements 60 are
coupled together to form an off-shore platform for a wind turbine that is
located in the ocean. These platforms call for high stiffness and high
damping. The present passive structural system, without active control
elements, can be easily incorporated into existing structures of this
sort and provide the benefits of reliability, simple construction, and
low cost.

[0029] A perspective view of one of the structural elements is shown in
detail, along with an end view of the element. The structural element can
be, for example, a rod, bar, beam, or plate; in this example, the
structural element is a hollow tube-shaped beam. In this example, each of
the bi-stable sub-structures 62 comprise a buckled column 64 which spans
the hollow interior of structural element 60, and is oriented
perpendicular to the tube's longitudinal axis. Pairs of buckled columns
which intersect to form an X-shaped pattern (as shown in FIG. 6) are
preferred. Buckled columns 64 are preferably "constrained buckled"
columns; i.e., they are in a "ready-to-snap-through" configuration. Here,
the columns have two equilibrium states: in the presence of a sufficient
amount of vibration energy, the buckled column will switch or
"snap-through" between one of its equilibrium states and the other. The
triggering of snap-through preferably occurs over a broad band of
excitation frequencies. A structure can dissipate a significant amount of
energy during this snap-through motion.

[0030] Each of the bi-stable sub-structures may further comprise a
concentrated mass 66 at the intersection of the buckled columns 64. The
motion of buckled columns 64 during transitions between their equilibrium
states dissipates at least a portion of the vibration energy; when the
concentrated masses snap-through, they experience a large velocity,
resulting in additional energy dissipation.

[0031] The present passive structural system may be intentionally
`mistuned`, such that when the system is subjected to energy that gives
rise to vibration, the vibration energy is substantially confined to
localized regions within the structural system. When the structure is
mistuned in this way, a tailored localization mode can be created which
exhibits large amplitude magnification in comparison with a periodic,
non-mistuned counterpart; a specifically designed mistuned profile can be
tailored to enable structural systems to adapt to varying loads.
Bi-stable sub-structures 62 may then be located in those localized
regions and arranged to dissipate the localized vibration energy. When so
arranged, the underlying load-bearing structural element provides high
stiffness, and the bi-stable sub-structures placed in localized regions
provide high damping.

[0032] One possible way to mistune a passive structural system and thereby
localize its vibration energy is shown in FIG. 6. Periodic appendage
sub-structures 70 may be coupled to the structural element. In this
example, the structural element is tube-shaped, and the appendage
sub-structures are rings which are coupled to and encircle the tube at
regular intervals; these external encircling rings are arranged to move
along the tube's longitudinal axis when subjected to vibration and
thereby dissipate at least a portion of the vibration energy. When so
arranged, the localized region to which vibration is confined would
typically be a specific ring (or several rings) which oscillate at a much
larger amplitude than the other rings, and would include the whole cross
section of the ring. As a result of vibration in a particular localized
region, the snap-through sub-structures in that region vibrate
significantly.

[0033] To mistune the structure, discrepancies can be introduced between
these periodic appendage sub-structures with variations in their
geometric parameters or material properties. These discrepancies can give
rise to a drastically different dynamic response than that of a perfect
periodic structure, leading to the confinement of vibration to small
geometric regions--i.e., localization. Vibration localization in a
periodic structure is generally undesirable, as it can cause components
in the localized areas to vibrate with a large amplitude and possibly
fail from high-cycle fatigue. Here, however, this vibration localization
is capitalized upon: bi-stable sub-structures are located in the
localized regions and arranged to dissipate the localized vibration
energy. In this way, a high stiffness, high damping structure can be
provided without active control elements.

[0034] A layer may be imposed between each encircling ring 70 and
structural element 60, to couple the ring to the structural element and
to serve as an additional damping element. For example, in the embodiment
shown in FIG. 6, there is a coupling elastic and damping material layer
72 between each ring and the surface of structural element 60. Layers 72
have respective material properties; one way in which mistuning can be
accomplished is to ensure that one or more material properties of layers
72 vary from layer to layer. For example, the stiffness and/or damping
coefficient of layers 72 can be made to vary from layer to layer.

[0035] Encircling rings 70 have respective parameters. Another way in
which mistuning can be effected is by having one or more ring parameter
vary from ring to ring. For example, encircling ring diameter and/or
encircling ring weight (e.g., rings having respective diameters of 0.5,
0.5, 0.52, 0.51, 0.5 cm, etc. and or rings with slightly different
densities) could be made to vary from ring to ring.

[0036] Another possible technique to mistune the structural element is to
arrange encircling rings 70 so that they are distributed at unequal
intervals along the axial length of structural element 60; the unequal
intervals result in the element being mistuned.

[0037] The damping mechanisms--here, coupling elastic and damping material
layer 72 and snap-through sub-structures 64--become the most effective
when they are applied to designated areas where the vibration energy is
confined. This confinement technique can suppress vibration much more
effectively than many traditional methods.

[0038] A passive structural system as described herein may also include a
structural link (not shown) which couples the periodic appendage
sub-structures together. For example, a structural link could be used to
couple encircling rings 70 to each other, which serves to disperse the
vibration energy over a larger area. A structural link might also be used
to couple together periodic bi-stable sub-structures 64.

[0039] The methodology described herein to construct a high stiffness,
high damping structural element can be further extended to more generic
structural elements such as torsional bars, bending beams, compression or
bending plates, etc., that form the basis for various 2-D and 3-D
structural systems. The methodology can be readily utilized to develop a
whole library of mistuned periodic structural elements exhibiting high
stiffness and high damping over a wide spectrum of loading range for
different applicable environments. It should also be noted that bi-stable
sub-structures as described herein can be arranged such that they can be
retrofitted into existing structural frame elements.

[0040] In addition to using conventional visco-elastic materials (such as
silicone rubber) to dissipate vibration energy, other novel units can
also be installed to dissipate energy more effectively. Snap-through or
constrained buckled columns are just a few examples to be incorporated
into this structural logic system.

[0041] Passive structural elements as described herein have many possible
applications. In addition to the off-shore platform application discussed
above, such structures might find use, for example, within aerospace
engines and components, to improve engine reliability and reduce noise by
reducing vibration. Another possible application would be within high
sensitivity electronic systems and instrumentation which calls for low
vibration control. In general, the present passive structural system may
be used with any structure for which vibration is to be damped.

[0042] While particular embodiments of the invention have been shown and
described, numerous variations and alternate embodiments will occur to
those skilled in the art. Accordingly, it is intended that the invention
be limited only in terms of the appended claims.